Anchor Papers ~ Algebra/Data Analysis ~ Item 30


	Item 30 Anchor Papers

Paul asked 50 randomly selected eleventh-grade students to choose their favorite candidate for class president. The survey results are shown in the table below.

Complete the following in the Answer Book:

There are 300 eleventh-grade students at Paul's school. Based on the survey results, how many votes will Marie expect to receive? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Using the survey results, Paul claims that Bertha will receive 2 more votes than Nick in the election. Is Paul correct? Use mathematics to justify your answer.
Loren asked the same question in another survey. She asked 50 randomly selected eleventh-grade chorus students to choose their favorite candidate for class president. Will you expect Loren's survey or Paul's survey to give more reliable results? Use mathematics to justify your answer.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The number of votes for Marie (72 votes) is correct. The explanation supports the solution, but is incomplete (taking the total votes and divided Marie's votes into it and got .24. I took .24 and multiplied it). No response is provided for the second or third parts of the question. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The number of votes for Marie (25) is incorrect, and no explanation is given. Although the student states that Paul is incorrect, the justification reveals a flaw in reasoning (Bertha will recieve 2 less votes than Nick will). The student believes that Paul's is the more reliable survey, and the justification supports the solution. (he is asking any eleventh grader. Loren, however, is asking just chorus students in the eleventh grade.) The response demonstrates a minimal understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates application of an incomplete strategy. While the number of votes for Marie (90 votes) is incorrect, the explanation does reveal an appropriate strategy. The student sets up an appropriate proportion to solve for x; however, 15 is used, instead of 12. Although the student states that Paul is incorrect, the justification reveals a flaw in reasoning (more people could vote for Nick than expected). Paul's survey is chosen as the more reliable, and the justification supports the solution. (Paul is asking a mix of everyone. Lorin is only asking one group of students.) The response demonstrates a conceptual understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates application of an incomplete strategy. The number of votes for Marie (72) is correct and the explanation supports the solution (I divided 300 by 50 and got 6 then multiplied that by 12). The student states that Paul is incorrect, and the justification supports the solution (Bertha will have 12 more votes than Nick). No response is given to the third part of the problem. This response demonstrates a conceptual understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie (72 votes) is correct; however, no explanation is given. The student states that Paul is incorrect, and the justification supports the solution (Bertha will get 96 votes while Nick only gets 84 votes). Paul's survey is chosen as the more reliable, and the justification supports the solution. (he survey 50 completely random 11^th graders for their choise on their class president, while Loren only surveyed 50 random CHORUS students, so not everyone has a fair chance at being surveyed by Loren.) The response demonstrates a clear understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie (72 votes) is correct. The fully developed explanation supports the solution. (12/50=.24 which is the probability of Marie's vote. 300 × .24 =72.) Although the student states that Paul is incorrect, the justification reveals a flaw in reasoning (other grade student might chose the other. They only have 50% to 50%. The survey only have 50 people, Bertha might get more than 2, or Nick will be more than Bertha). Paul's survey is chosen as the more reliable, and the justification supports the solution (some students are not chorus students. Loren's idea is not equaly likely to all the students). The response demonstrates a clear understanding and analysis of the problem.
Score Level 4 Anchor Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of votes for Marie is correct. The symbolic explanation is clearly presented, fully developed, and supports the solution; the student sets up the appropriate proportion and solves for x. The student believes that Paul is incorrect. The fully developed symbolic justification supports the solution; the student sets up proportions to find the number of votes Bertha and Nick would expect, finds the difference, and notes that Nick would receive 12 votes less than Bertha. Paul's survey is chosen as the more reliable, and the justification is fully developed. (he surveyed diff. kinds of kids. Loren only surveyed a sample space of kids, chorus students.) The response demonstrates a complete understanding and analysis of the problem.
Score Level 4 Anchor Paper
This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The number of votes for Marie is correct (72 votes). The explanation is clearly presented, fully developed and supports the solution (To get 12/50 to equal ?/300 you must multiply the top and bottom #s by 6. 12/50 • 6/6= 72/300). The student states that Paul is incorrect and the justification is fully developed; the student sets up proportions to find the number of votes Bertha and Nick would expect and then states (Nick is expected to get 84 votes and Bertha is expected to get 96). Paul's survey is chosen as the more reliable. The justification is fully developed (it is not biased toward any school groups like Loren's is toward the chorus). This response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 30

Paul asked 50 randomly selected eleventh-grade students to choose their favorite candidate for class president. The survey results are shown in the table below.

Complete the following in the Answer Book:

There are 300 eleventh-grade students at Paul's school. Based on the survey results, how many votes will Marie expect to receive? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Using the survey results, Paul claims that Bertha will receive 2 more votes than Nick in the election. Is Paul correct? Use mathematics to justify your answer.
Loren asked the same question in another survey. She asked 50 randomly selected eleventh-grade chorus students to choose their favorite candidate for class president. Will you expect Loren's survey or Paul's survey to give more reliable results? Use mathematics to justify your answer.

Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The number of votes for Marie (72 votes) is correct. The explanation supports the solution, but is incomplete (taking the total votes and divided Marie's votes into it and got .24. I took .24 and multiplied it). No response is provided for the second or third parts of the question. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The number of votes for Marie (25) is incorrect, and no explanation is given. Although the student states that Paul is incorrect, the justification reveals a flaw in reasoning (Bertha will recieve 2 less votes than Nick will). The student believes that Paul's is the more reliable survey, and the justification supports the solution. (he is asking any eleventh grader. Loren, however, is asking just chorus students in the eleventh grade.) The response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates application of an incomplete strategy. While the number of votes for Marie (90 votes) is incorrect, the explanation does reveal an appropriate strategy. The student sets up an appropriate proportion to solve for x; however, 15 is used, instead of 12. Although the student states that Paul is incorrect, the justification reveals a flaw in reasoning (more people could vote for Nick than expected). Paul's survey is chosen as the more reliable, and the justification supports the solution. (Paul is asking a mix of everyone. Lorin is only asking one group of students.) The response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates application of an incomplete strategy. The number of votes for Marie (72) is correct and the explanation supports the solution (I divided 300 by 50 and got 6 then multiplied that by 12). The student states that Paul is incorrect, and the justification supports the solution (Bertha will have 12 more votes than Nick). No response is given to the third part of the problem. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie (72 votes) is correct; however, no explanation is given. The student states that Paul is incorrect, and the justification supports the solution (Bertha will get 96 votes while Nick only gets 84 votes). Paul's survey is chosen as the more reliable, and the justification supports the solution. (he survey 50 completely random 11^th graders for their choise on their class president, while Loren only surveyed 50 random CHORUS students, so not everyone has a fair chance at being surveyed by Loren.) The response demonstrates a clear understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie (72 votes) is correct. The fully developed explanation supports the solution. (12/50=.24 which is the probability of Marie's vote. 300 × .24 =72.) Although the student states that Paul is incorrect, the justification reveals a flaw in reasoning (other grade student might chose the other. They only have 50% to 50%. The survey only have 50 people, Bertha might get more than 2, or Nick will be more than Bertha). Paul's survey is chosen as the more reliable, and the justification supports the solution (some students are not chorus students. Loren's idea is not equaly likely to all the students). The response demonstrates a clear understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of votes for Marie is correct. The symbolic explanation is clearly presented, fully developed, and supports the solution; the student sets up the appropriate proportion and solves for x. The student believes that Paul is incorrect. The fully developed symbolic justification supports the solution; the student sets up proportions to find the number of votes Bertha and Nick would expect, finds the difference, and notes that Nick would receive 12 votes less than Bertha. Paul's survey is chosen as the more reliable, and the justification is fully developed. (he surveyed diff. kinds of kids. Loren only surveyed a sample space of kids, chorus students.) The response demonstrates a complete understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The number of votes for Marie is correct (72 votes). The explanation is clearly presented, fully developed and supports the solution (To get 12/50 to equal ?/300 you must multiply the top and bottom #s by 6. 12/50 • 6/6= 72/300). The student states that Paul is incorrect and the justification is fully developed; the student sets up proportions to find the number of votes Bertha and Nick would expect and then states (Nick is expected to get 84 votes and Bertha is expected to get 96). Paul's survey is chosen as the more reliable. The justification is fully developed (it is not biased toward any school groups like Loren's is toward the chorus). This response demonstrates a complete understanding and analysis of the problem.